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%I #25 Feb 03 2020 15:29:01
%S 3,9,27,57,99,153,219,297,387,489,603,729,867,1017,1179,1353,1539,
%T 1737,1947,2169,2403,2649,2907,3177,3459,3753,4059,4377,4707,5049,
%U 5403,5769,6147,6537,6939,7353,7779,8217,8667,9129,9603,10089,10587,11097,11619
%N a(n) = 3*(2*n^2 + 1).
%C a(n) is also the number of Arnoux-Rauzy factors of length (n+1) over a 3-letter alphabet. - Genevieve Paquin (genevieve.paquin(AT)univ-savoie.fr), Nov 07 2008
%H Harvey P. Dale, <a href="/A097803/b097803.txt">Table of n, a(n) for n = 0..1000</a>
%H F. Mignosi and L. Q. Zamboni, <a href="http://dx.doi.org/10.4064/aa101-2-4">On the number of Arnoux-Rauzy words</a>, Acta arith., 101 (2002), no. 2, 121-129. [From Genevieve Paquin (genevieve.paquin(AT)univ-savoie.fr), Nov 07 2008]
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(0)=3, a(1)=9, a(2)=27, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, Dec 29 2011
%F G.f.: -((3*(3*x^2+1))/(x-1)^3). - _Harvey P. Dale_, Dec 29 2011
%t Table[ 3(2*n^2 + 1), {n, 0, 44}] (* _Robert G. Wilson v_, Aug 26 2004 *)
%t 3(2Range[0,50]^2+1) (* or *) LinearRecurrence[{3,-3,1},{3,9,27},50] (* _Harvey P. Dale_, Dec 29 2011 *)
%o (PARI) a(n)=3*(2*n^2+1) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A097802.
%K nonn,easy
%O 0,1
%A _George E. Antoniou_, Aug 25 2004
%E More terms from _Robert G. Wilson v_ and Mark Hudson (mrmarkhudson(AT)hotmail.com), Aug 26 2004
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